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Geometric Progressions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsGeometric Progressions2 Marks
Question
If a, b, c are in G.P., Prove that $\log \text{a}, \log \text{b},\log\text{c}$ are in A.P.
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Answer

Here, a, b, c are in G.P.
$\text{b}^2=\text{ac}\cdots(\text{i})$
Now, $2\log\text{b}=\log\text{b}^2$
$=\log\text{ ac}$
$2\log\text{b}=\log\text{a}+\log\text{c}$
$\log\text{b}-\log\text{a}=\log\text{c}-\log\text{b}$
$\Rightarrow\log\text{a},\log\text{b}\log\text{c},\text{ are in A.P.}$

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